*There are no fixtures in nature.*

The universe is fluid and volatile.

Permanence is but a word of degrees.~ Ralph Waldo Emerson (1803-1882)

The universe is fluid and volatile.

Permanence is but a word of degrees.

To perceive something as fixed when it is actually transient is usually considered a foolish mistake. Yet, we do it all the time in investing when we treat historical data series as stationary — i.e., in statistical terms, as if their means and variances are constant over time. In reality, nearly all of the historical data sets we encounter as investors are non-stationary — their means and their variances in one time period do not apply in another. Thus the illusion of The Long-Term Average.

**FIRST VIEW:**As one example, charted below is a time series showing the estimated, real "risk-free" interest rate over eight centuries, from 1314-2017. Drawn across the chart is a dashed line (in red) indicating the 704-year average, at 4.78%. Consciously or unconsciously, this line registers in most investors' minds as the "normal" historical real interest rate. Using this chart, it's easy to get the impression that interest rates are a stationary series with a fixed mean — leading one to naturally wonder, "When will today's rates start reverting back toward their long-term average?"

Source: Bank of England

**SECOND VIEW:**Statistical tests of this same data would show that, in fact, interest rates are NOT a stationary time series. As a simple proof, when the average interest rate for each of the eight centuries is calculated and charted (in light blue, below), we see that the mean value changes, sometimes dramatically, from one century to the next. This is the very definition of a non-stationary data series — and it makes the idea of "reversion to the mean" for interest rates nonsensical. What mean? Which time period?

Source: Bank of England

**CONCLUSION:**Non-stationary historical data series are by far the norm in finance and investing. So the next time a pundit shows you a chart like the one below, suggesting that "U.S. stocks are dangerously overvalued today, compared with their historical average," I'd encourage you to kindly ignore their comments and remember the illusion of The Long-Term Average.

Source: Shiller Data